Problem: A piano teacher has $4\dfrac12$ hours available to teach in a night. Each lesson will last $1\dfrac12$ hours. How many lessons can the teacher schedule in a night?
Solution: We can think about this problem like this: $ {\text{number of lessons}} = {\text{time available}} \div {\text{time spent each lesson}}$ ${\text{?}} = {4\dfrac12 \text{hours}} \div {1\dfrac{1}{2} \text{hours}}$ $\phantom{?} = {\dfrac92 \text{hours}} \div {\dfrac{3}{2} \text{hours}} ~~~~~~~{\text{Rewrite } {4\dfrac12} \text{ as } { \dfrac92} \text{ and }{1\dfrac{1}{2}} \text{ as } {\dfrac{3}{2}}}$ $\phantom{?} = {\dfrac92} \times \dfrac{2}{3} ~~~~~~~{\text{Rewrite dividing by} {\dfrac{3}{2}} \text{ as multiplying by} \dfrac{2}{3}}$ $\phantom{?} =\dfrac{9 \times 2}{2 \times 3}$ $\phantom{?} =\dfrac{18}{6}$ $\phantom{?} = {3 \text{ lessons}}$ The teacher can schedule $3$ lessons.